All low order H controllers with covariance upper bound
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This paper obtains a parametrization of the set of all stabilizing controllers of order equal to or less than the plant, which yield a specified H norm bound to the closed loop transfer matrix. A Lyapunov based approach to H control problems yields a parametrization in terms of the Lyapunov matrix which carries many system properties such as H2 performance, covariance bounds, system entropy at infinity, etc. Since the freedom in the parametrization is explicit in arbitrary matrices of fixed dimensions, the advantage over the existing Q-parametrization is the finiteness of the design parameter space. It is shown that low order H suboptimal controllers can be designed by solving two Riccati equations which are uncoupled in one direction. Perspectives on the new parametrization are discussed considering the simple full order controller case. A numerical example of robust control design with an H2 performance criterion is presented for a benchmark problem.
